Dynamical theories of dark-field imaging using diffusely scattered electrons in STEM and TEM

Dynamical theories of atomic number sensitive image (or Z-contrast image) formed by thermal diffusely scattered (TDS) electrons are proposed based on first-principles considerations. `Exact' theories are derived for simulating images obtained either in scanning transmission electron microscopy (STEM) using an annular dark-field detector or in transmission electron microscopy (TEM) using an on-axis objective aperture under hollow-cone beam illumination. The atom thermal vibrations are described using lattice dynamics with consideration of phase correlations. The effects that are comprehensively covered in the theory include: dynamical diffraction of the beam before and after TDS, thickness-dependent beam broadening or channelling, Huang scattering from defect regions, coherence of the thermal diffusely scattered electrons generated from the atomic layers packed within the coherent length, multiphonon and multiple phonon excitations, and the detector geometry. Simplified theories have been derived from this unified approach under various approximations. It has been shown that the incoherent imaging theory is a much simplified case of the practical imaging condition, and can be applied only for qualitative image interpretation. The coherent length in the z direction varies with the change of atomic mass in the column. It is thus possible that the z coherence may disappear for heavy elements. Finally, the theory of Huang scattering in high-angle dark-field TEM imaging has been illustrated, and the theoretically expected results have been observed experimentally.